The Balanced Discrete Weibull Distribution and Its Corresponding Integer-value Autoregressive Model: Properties, Estimation and Analysis of Counting Death of COVID-19 Data

In this paper, we introduce a new discrete Weibull distribution based on the balanced discretization method, which preserves the partial moments between the two discrete and continuous versionsof the distributions. Some statistical features of the new distribution and different kinds of dispersion ofthe proposed distribution are presented based on various selections of parameters. In addition to introducing the new version of balanced discrete Weibull, we provide the integer-valued autoregressive modelwith the innovation of the proposed discrete distribution and evaluate different methods for estimating themodel parameters. Using the counts of death of the COVID-19 data in Cuba, Malawi and Uzbekistan, weappraise the performance of the new process in fitting real data to some classical integer-valued autoregressive models. Finally, the forecasting of the process is checked based on real data using both classicaland sieve bootstrap approaches